Mechanics of Time-Dependent Materials

, Volume 15, Issue 3, pp 277–291 | Cite as

Plastic deformation in multilayered thin films during indentation unloading: a modeling analysis incorporating viscoplastic response



The indentation behavior of metal/ceramic multilayered thin films is studied numerically using the finite element method. The axisymmetric model consists of alternating aluminum (Al) and silicon carbide (SiC) layers above a silicon (Si) substrate, with the rate-dependent viscoplastic response of Al accounted for. Different unloading rates, with and without a hold period at the peak indentation load, are considered. Attention is devoted to plastic deformation in the Al layers during the unloading phase of indentation. It is found that the hold period stabilizes the deformation so the unloading response becomes insensitive to the unloading rate. However, significant parts of the Al layers under indentation still experience plastic deformation during unloading, due to the mechanical constraint imposed by the hard SiC layers. Consequently unloading is no longer an elastic event in this heterogeneous material system. The unloading induced plasticity is further analyzed by tracking the stress and strain histories inside the material throughout the course of indentation.


Indentation Nanoindentation Finite element modeling Thin films Plastic deformation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bucaille, J.L., Stauss, S., Schwaller, P., Michler, J.: A new technique to determine the elastoplastic properties of thin metallic films using sharp indenters. Thin Solid Films 447, 239–245 (2004) CrossRefGoogle Scholar
  2. Cheng, Y.-T., Cheng, C.-M.: Can stress-strain relationship be obtained from indentation curves using conical and pyramidal indenters? J. Mater. Res. 14, 3493–3496 (1999) CrossRefGoogle Scholar
  3. Dao, M., Chollacoop, N., Van Vliet, K.J., Venkatesh, T.A., Suresh, S.: Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899–3918 (2001) CrossRefGoogle Scholar
  4. Deng, X., Chawla, N., Chawla, K.K., Koopman, M., Chu, J.P.: Mechanical behavior of multilayered nanoscale metal-ceramic composites. Adv. Eng. Mater. 7, 1099–1108 (2005) CrossRefGoogle Scholar
  5. Fang, N.: A new quantitative sensitivity analysis of the flow stress of 18 engineering materials in machining. J. Mater. Sci. Technol. 127, 192–196 (2005) Google Scholar
  6. Fischer-Cripps, A.C.: Nanoindentation. Springer, New York (2002) Google Scholar
  7. Gouldstone, A., Chollacoop, N., Dao, M., Li, J., Minor, A.M., Shen, Y.-L.: Indentation across size scales and disciplines: Recent developments in experimentation and modeling. Acta Mater. 55, 4015–4039 (2007) CrossRefGoogle Scholar
  8. Lan, H., Venkatesh, T.A.: Determination of the elastic and plastic properties of materials through instrumented indentation with reduced sensitivity. Acta Mater. 55, 2025–2041 (2007) CrossRefGoogle Scholar
  9. Lide, D.R.: Handbook of Chemistry and Physics, 76th edn. CRC Press, Boca Raton (1995) Google Scholar
  10. Oliver, W.C., Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583 (1992) CrossRefGoogle Scholar
  11. Schuh, C.A.: Nanoindentation studies of materials. Mater. Today 9(5), 32–40 (2006) CrossRefGoogle Scholar
  12. Stone, D.S., Jakes, J.E., Puthoff, J., Elmustafa, A.A.: Analysis of indentation creep. J. Mater. Res. 25, 611–621 (2010) CrossRefGoogle Scholar
  13. Tang, G.: Indentation analysis and mechanical modeling of multilayered nanocomposites. Doctoral Dissertation, University of New Mexico (2009) Google Scholar
  14. Tang, G., Shen, Y.-L., Chawla, N.: Plastic deformation during indentation unloading in multilayered materials. J. Appl. Phys. 104, 116102 (2008) CrossRefGoogle Scholar
  15. Tang, G., Singh, D.R.P., Shen, Y.-L., Chawla, N.: Elastic properties of metal-ceramic nanolaminates measured by nanoindentation. Mater. Sci. Eng. A 502, 79–84 (2009) CrossRefGoogle Scholar
  16. Tang, G., Shen, Y.-L., Singh, D.R.P., Chawla, N.: Indentation behavior of metal-ceramic multilayers at the nanoscale: Numerical analysis and experimental verification. Acta Mater. 58, 2033–2044 (2010) CrossRefGoogle Scholar
  17. Zhao, M., Chen, X., Xiang, Y., Vlassak, J.J., Lee, D., Ogasawara, N., Chiba, N., Gan, Y.X.: Measuring elastoplastic properties of thin films on an elastic substrate using sharp indentation. Acta Mater. 55, 6260–6274 (2007) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, B. V. 2011

Authors and Affiliations

  1. 1.Department of Mechanical and Computer-Aided EngineeringSt. John’s UniversityTaipeiTaiwan
  2. 2.Department of Mechanical EngineeringUniversity of New MexicoAlbuquerqueUSA

Personalised recommendations